The initial entropy density profile which serves as an input for our hydrodynamic calculation is obtained by taking an initial state average of 10000 events with random nucleonic positions at impact parameter \(b \approx 0\)  fm. We modify the (2+1) dimensional ideal relativistic hydrodynamic model [1]} to obtain the space-time evolution of the above initial entropy distribution at the mid-rapidity. The initial flow velocity component, \(v_x\)  and \(v_y\)  are taken as zero. For the sake of simplicity, we take the value of initial thermalization time as \(\tau _0=\)  0.17 fm/\(c\)  which has been used for the \(\rm {Au+Au}\)  collisions at RHIC [2]}, [3]}, although one may expect a larger value of initial thermalization time for small systems. A lattice-based equation of state [4]} is used and we consider a constant temperature freeze-out at 160 MeV. The same freeze-out temperature (\(T_f\) ) is used in earlier studies of Au+Au collisions at RHIC using the same hydrodynamical model [5]}, [6]}, [3]}, [8]}.
